In this paper,the dynamics of a Leslie-Gower predator-prey model with weak nonlin-ear harvesting and prey-taxis is discussed.By comparing and analyzing the differences between ordinary differential systems and chemota...In this paper,the dynamics of a Leslie-Gower predator-prey model with weak nonlin-ear harvesting and prey-taxis is discussed.By comparing and analyzing the differences between ordinary differential systems and chemotaxis systems in the stability of equilibrium points,the influence mechanism of chemotaxis on the dynamic behavior of the system is deeply studied.Theoretical analysis shows that chemotaxis significantly changes the stability characteristics of the system,and the reliability of theoretical results is further verified by numerical simulation.展开更多
We present a novel nonlinear state transition model for inositol 1,4,5-trisphosphate receptors(IP_(3)Rs)that incorporates a pre-activated state,as suggested by electron microscopy observations.Our model provides a the...We present a novel nonlinear state transition model for inositol 1,4,5-trisphosphate receptors(IP_(3)Rs)that incorporates a pre-activated state,as suggested by electron microscopy observations.Our model provides a theoretical framework for the biphasic Ca^(2+)dependence of IP_(3)Rs and accurately reproduces their experimentally observed state distribution under saturating IP_(3) conditions.By integrating receptor dynamics with cytoplasmic and endoplasmic reticulum(ER)calcium exchange,we simulate IP_(3)R-mediated Ca^(2+)oscillations governed by six key conformational states.A pivotal finding is that IP_(3)regulates these oscillations in a switch-like manner:once a critical IP_(3) concentration is reached,the system abruptly transitions to sustained,constant-amplitude oscillations that quickly terminate when the concentration exceeds a secondary threshold.These results underscore the crucial role of the pre-activated state in modulating calcium signaling.展开更多
A class of nonlinear and continuous type Leontief model and its corresponding conditional input-output equation are introduced, and two basic problems under the so called positive or negative boundary assumption are p...A class of nonlinear and continuous type Leontief model and its corresponding conditional input-output equation are introduced, and two basic problems under the so called positive or negative boundary assumption are presented. By approaches of nonlinear analysis some solvability results of this equation and continuous perturbation properties of the relative solution sets are obtained, and some economic significance are illustrated by the remark.展开更多
A nonlinear multi-scale interaction(NMI)model was proposed and developed by the first author for nearly 30 years to represent the evolution of atmospheric blocking.In this review paper,we first review the creation and...A nonlinear multi-scale interaction(NMI)model was proposed and developed by the first author for nearly 30 years to represent the evolution of atmospheric blocking.In this review paper,we first review the creation and development of the NMI model and then emphasize that the NMI model represents a new tool for identifying the basic physics of how climate change influences mid-to-high latitude weather extremes.The building of the NMI model took place over three main periods.In the 1990s,a nonlinear Schr?dinger(NLS)equation model was presented to describe atmospheric blocking as a wave packet;however,it could not depict the lifetime(10-20 days)of atmospheric blocking.In the 2000s,we proposed an NMI model of atmospheric blocking in a uniform basic flow by making a scale-separation assumption and deriving an eddyforced NLS equation.This model succeeded in describing the life cycle of atmospheric blocking.In the 2020s,the NMI model was extended to include the impact of a changing climate mainly by altering the basic zonal winds and the magnitude of the meridional background potential vorticity gradient(PVy).Model results show that when PVy is smaller,blocking has a weaker dispersion and a stronger nonlinearity,so blocking can be more persistent and have a larger zonal scale and weaker eastward movement,thus favoring stronger weather extremes.However,when PVy is much smaller and below a critical threshold under much stronger winter Arctic warming of global warming,atmospheric blocking becomes locally less persistent and shows a much stronger westward movement,which acts to inhibit local cold extremes.Such a case does not happen in summer under global warming because PVy fails to fall below the critical threshold.Thus,our theory indicates that global warming can render summer-blocking anticyclones and mid-to-high latitude heatwaves more persistent,intense,and widespread.展开更多
In this paper, two types of mathematical models are developed to describe the dynamics of large-scale nonlinear systems, which are composed of several interconnected nonlinear subsystems. Each subsystem can be describ...In this paper, two types of mathematical models are developed to describe the dynamics of large-scale nonlinear systems, which are composed of several interconnected nonlinear subsystems. Each subsystem can be described by an input-output nonlinear discrete-time mathematical model, with unknown, but constant or slowly time-varying parameters. Then, two recursive estimation methods are used to solve the parametric estimation problem for the considered class of the interconnected nonlinear systems. These methods are based on the recursive least squares techniques and the prediction error method. Convergence analysis is provided using the hyper-stability and positivity method and the differential equation approach. A numerical simulation example of the parametric estimation of a stochastic interconnected nonlinear hydraulic system is treated.展开更多
Data-driven reduced-order modeling opens new avenues of understanding,predicting,controlling,and optimizing system behavior.Simple systems may have state spaces in which sparse human-interpretable dynamical systems ca...Data-driven reduced-order modeling opens new avenues of understanding,predicting,controlling,and optimizing system behavior.Simple systems may have state spaces in which sparse human-interpretable dynamical systems can be identified.This approach has been pioneered by Brunton et al.(2016,PNAS)with sparse identification of nonlinear dynamics.Complex systems,however,cannot be expected to benefit from such simple analytical descriptions.Yet,smoothness may be exploited by analytical local descriptions.In this paper,we identify a clusterwise polynomial dynamics from time-resolved snapshot data.The full state space is partitioned into clusters with a reduced-order polynomial description for each cluster and a global patching strategy.The resulting clusterwise modeling is entirely data-driven and requires no prior knowledge of the system dynamics.We illustrate the approach on the well-known chaotic Lorenz and Rössler systems,on the more challenging chaotic fluid flow dynamics of higher state-space dimensions,on a noisy electrocardiogram signal,and finally on the time evolution of the monthly sunspot number.Clusterwise modeling offers a powerful and interpretable paradigm for dynamical modeling.Nonlinear dynamics can be approximated by assembling many simple local models of different resolutions,opening new paths to understand and control intricate nonlinearities.展开更多
An optimal fuzzy tracking synthesis for nonlinear discrete-time descriptor systems is discussed through the Parallel Distributed Compensation(PDC)approach and the Proportional-Difference(P-D)feedback framework.Based o...An optimal fuzzy tracking synthesis for nonlinear discrete-time descriptor systems is discussed through the Parallel Distributed Compensation(PDC)approach and the Proportional-Difference(P-D)feedback framework.Based on the Takagi-Sugeno Fuzzy Descriptor Model(T-SFDM),a nonlinear discrete-time descriptor system is represented as several linear fuzzy subsystems,which facilitates the linear P-D feedback technique and streamlines the fuzzy controller design process.Leveraging the P-D feedback fuzzy controller,the closed-loop T-SFDM can be transformed into a standard system that guarantees non-impulsiveness and causality for the nonlinear discrete-time descriptor system.In view of the disturbance problems,a passive performance constraint is incorporated into the fuzzy tracking synthesis to achieve dissipativity of disturbance energy.To achieve a better balance between state and control responses,the H2 performance requirement is considered and a minimization constraint is applied to optimize the H2 index.It is observed that there is a lack of research focusing on both disturbance and control input issues in nonlinear descriptor systems.Extending the Lyapunov theory,a stability analysis method is proposed for the tracking purpose with the combination of the free-weighting matrix to relax the analysis process while complying multiple performance constraints.Finally,two simulation examples are presented to demonstrate the feasibility and applicability of the proposed approach in practical control scenarios for nonlinear descriptor systems.展开更多
In this paper,we propose a multiphysics finite element method for a nonlinear poroelasticity model with nonlinear stress-strain relation.Firstly,we reformulate the original problem into a new coupled fluid system-a ge...In this paper,we propose a multiphysics finite element method for a nonlinear poroelasticity model with nonlinear stress-strain relation.Firstly,we reformulate the original problem into a new coupled fluid system-a generalized nonlinear Stokes problem of displacement vector field related to pseudo pressure and a diffusion problem of other pseudo pressure fields.Secondly,a fully discrete multiphysics finite element method is performed to solve the reformulated system numerically.Thirdly,existence and uniqueness of the weak solution of the reformulated model and stability analysis and optimal convergence order for the multiphysics finite element method are proven theoretically.Lastly,numerical tests are given to verify the theoretical results.展开更多
We study the thermodynamic properties of the classical one-dimensional generalized nonlinear Klein-Gordon lattice model(n≥2)by using the cluster variation method with linear response theory.The results of this method...We study the thermodynamic properties of the classical one-dimensional generalized nonlinear Klein-Gordon lattice model(n≥2)by using the cluster variation method with linear response theory.The results of this method are exact in the thermodynamic limit.We present the single-site reduced densityρ^((1))(z),averages such as(z^(2)),<|z^(n)|>,and<(z_(1)-z_(2))^(2)>,the specific heat C_(v),and the static correlation functions.We analyze the scaling behavior of these quantities and obtain the exact scaling powers at the low and high temperatures.Using these results,we gauge the accuracy of the projective truncation approximation for theφ^(4)lattice model.展开更多
During strike-slip fault dislocation,multiple fault planes are commonly observed.The resulting permanent ground deformation can lead to profound structural damage to tunnels.However,existing analytical models do not c...During strike-slip fault dislocation,multiple fault planes are commonly observed.The resulting permanent ground deformation can lead to profound structural damage to tunnels.However,existing analytical models do not consider multiple fault planes.Instead,they concentrate the entire fault displacement onto a single fault plane for analysis,thereby giving rise to notable errors in the calculated results.To address this issue,a refined nonlinear theoretical model was established to analyze the mechanical responses of the tunnels subjected to multiple strike-slip fault dislocations.The analytical model considers the number of fault planes,nonlinear soil‒tunnel interactions,geometric nonlinearity,and fault zone width,leading to a significant improvement in its range of applicability and calculation accuracy.The results of the analytical model are in agreement,both qualitatively and quantitatively,with the model test and numerical results.Then,based on the proposed theoretical model,a sensitivity analysis of parameters was conducted,focusing on the variables such as the number of fault planes,fault plane distance(d),fault displacement ratio(η),burial depth(C),crossing angle(β),tunnel diameter(D),fault zone width(Wf),and strike-slip fault displacement(Δfs).The results show that the peak shear force(Vmax),bending moment(Mmax),and axial force(Nmax)decrease with increasing d.The Vmax of the tunnel is found at the fault plane with the largest fault displacement.C,D,andΔfs contribute to the increases in Vmax,Mmax,and Nmax.Additionally,increasing the number of fault planes reduces Vmax and Mmax,whereas the variation in Nmax remains minimal.展开更多
Dear Editor,Aiming at the consensus tracking problem of a class of unknown heterogeneous nonlinear multiagent systems(MASs)with input constraints,a novel data-driven iterative learning consensus control(ILCC)protocol ...Dear Editor,Aiming at the consensus tracking problem of a class of unknown heterogeneous nonlinear multiagent systems(MASs)with input constraints,a novel data-driven iterative learning consensus control(ILCC)protocol based on zeroing neural networks(ZNNs)is proposed.First,a dynamic linearization data model(DLDM)is acquired via dynamic linearization technology(DLT).展开更多
Coordinate transformation models often fail to account for nonlinear and spatially dependent distortions,leading to significant residual errors in geospatial applications.Here,we propose a residual-based neural correc...Coordinate transformation models often fail to account for nonlinear and spatially dependent distortions,leading to significant residual errors in geospatial applications.Here,we propose a residual-based neural correction(RBNC)strategy,in which a neural network learns to model only the systematic distortions left by an initial geometric transformation.By focusing solely on residual patterns,RBNC reduces model complexity and improves performance,particularly in scenarios with sparse or structured control point configurations.We evaluate the method using both simulated datasets(with varying distortion intensities and sampling strategies)and real-world image georeferencing tasks.Compared with direct neural network coordinate converters and classical transformation models,RBNC delivers more accurate and stable results under challenging conditions,while maintaining comparable performance in ideal cases.These findings demonstrate the effectiveness of residual modelling as a light-weight and robust alternative for improving coordinate transformation accuracy.展开更多
Shoreline sand wave movement is one of the hot issues in coastal dynamics research.The nonlinear nearshore waves constitute the core driving force for shoreline sediment transport,significantly enhancing the lateral s...Shoreline sand wave movement is one of the hot issues in coastal dynamics research.The nonlinear nearshore waves constitute the core driving force for shoreline sediment transport,significantly enhancing the lateral sediment transport intensity and exerting an important influence on shoreline sand wave movement.By using the XBeach model,the evolution process of the profile of a typical sandy beach in Haizhou Bay under the action of nonlinear waves was simulated,and the comprehensive influence of wave nonlinearity on the lateral sediment transport and sand wave movement of the beach was analyzed.The results show that the nonlinearity of waves has a relatively significant impact on the sediment transport along the shoreline of Haizhou Bay.The sediment transport in the breakwave zone 500 meters offshore is frequent.The peak line of the sand wave moves towards the shore year by year,and the peak elevation increases year by year.Within the calculation range of the model,the net sediment transport to the sea shows a slightly eroded feature in the intertidal zone of the nearshore tidal flat of Haizhou Bay.The research results have important reference significance for grasping the erosion and topographic evolution laws of the nearshore beaches of Haizhou Bay.展开更多
In this paper,the authors propose a nonlinear dimension reduction technique based on Fréchet inverse regression to achieve sufficient dimension reduction for responses in metric spaces and predictors in Riemannia...In this paper,the authors propose a nonlinear dimension reduction technique based on Fréchet inverse regression to achieve sufficient dimension reduction for responses in metric spaces and predictors in Riemannian manifolds.The authors rigorously establish statistical properties of the estimators,providing formal proofs of their consistency and asymptotic behaviors.The effectiveness of our method is demonstrated through extensive simulations and applications to real-world datasets which highlight its practical utility for complex data with non-Euclidean structures.展开更多
This paper develops a feedforward neural network based input output model for a general unknown nonlinear dynamic system identification when only the inputs and outputs are accessible observations. In the developed m...This paper develops a feedforward neural network based input output model for a general unknown nonlinear dynamic system identification when only the inputs and outputs are accessible observations. In the developed model, the size of the input space is directly related to the system order. By monitoring the identification error characteristic curve, we are able to determine the system order and subsequently an appropriate network structure for systems identification. Simulation results are promising and show that generic nonlinear systems can be identified, different cases of the same system can also be discriminated by our model.展开更多
[Objective] The aim was to develop a nonlinear model of quantitative analysis of melamine content by infrared spectroscopy and provide theoretical basis for the nondestructive detection of melamine. [Method] According...[Objective] The aim was to develop a nonlinear model of quantitative analysis of melamine content by infrared spectroscopy and provide theoretical basis for the nondestructive detection of melamine. [Method] According to dynamics,mathematical modeling and optimization theory,linear and nonlinear models were respectively set up by taking an absorption peak of 1 550 cm-1 as characteristic absorption peak. [Result] The correlation coefficient of nonlinear model was 0.922 7 and the recovery was 96%,which showed that the nonlinear model was more accurate than linearity model with correlation coefficient of 0.904 9 and recovery of 557%. [Conclusion] It is feasible to determine melamine content by using the nonlinear model quantitatively.展开更多
A wavelet collocation method with nonlinear auto companding is proposed for behavioral modeling of switched current circuits.The companding function is automatically constructed according to the initial error distri...A wavelet collocation method with nonlinear auto companding is proposed for behavioral modeling of switched current circuits.The companding function is automatically constructed according to the initial error distribution obtained through approximating the input output function of the SI circuit by conventional wavelet collocation method.In practical applications,the proposed method is a general purpose approach,by which both the small signal effect and the large signal effect are modeled in a unified formulation to ease the process of modeling and simulation.Compared with the published modeling approaches,the proposed nonlinear auto companding method works more efficiently not only in controlling the error distribution but also in reducing the modeling errors.To demonstrate the promising features of the proposed method,several SI circuits are employed as examples to be modeled and simulated.展开更多
A classic hysteretic model, Preisach-Mayergoyz model （P-M model）, was used to calculate the nonlinear elastic deformation of magnesium （Mg） and cobalt （Co）. Mg and Co samples in cylinder shape were compressively...A classic hysteretic model, Preisach-Mayergoyz model （P-M model）, was used to calculate the nonlinear elastic deformation of magnesium （Mg） and cobalt （Co）. Mg and Co samples in cylinder shape were compressively tested by uniaxial test machine to obtain their stress—strain curves with hysteretic loops. The hysteretic loops do have two properties of P-M hysteretic systems： wiping out and congruency. It is proved that P-M model is applicable for the analysis of these two metals’ hysteresis. This model was applied on Mg at room temperature and Co at 300 ℃. By the P-M model, Co and Mg nonlinear elastic deformation can be calculated based on the stress history. The simulated stress—strain curves agree well with the experimental results. Therefore, the mechanical hysteresis of these two metals can be easily predicted by the classic P-M hysteretic model.展开更多
In order to detect whether the data conforms to the given model, it is necessary to diagnose the data in the statistical way. The diagnostic problem in generalized nonlinear models based on the maximum Lq-likelihood e...In order to detect whether the data conforms to the given model, it is necessary to diagnose the data in the statistical way. The diagnostic problem in generalized nonlinear models based on the maximum Lq-likelihood estimation is considered. Three diagnostic statistics are used to detect whether the outliers exist in the data set. Simulation results show that when the sample size is small, the values of diagnostic statistics based on the maximum Lq-likelihood estimation are greater than the values based on the maximum likelihood estimation. As the sample size increases, the difference between the values of the diagnostic statistics based on two estimation methods diminishes gradually. It means that the outliers can be distinguished easier through the maximum Lq-likelihood method than those through the maximum likelihood estimation method.展开更多
In this paper,a framework is established for nonlinear flutter and gust response analyses based on an efficient Reduced Order Model(ROM).The proposed method can be used to solve the aeroelastic response problems of wi...In this paper,a framework is established for nonlinear flutter and gust response analyses based on an efficient Reduced Order Model(ROM).The proposed method can be used to solve the aeroelastic response problems of wings containing geometric nonlinearities.A structural modeling approach presented herein describes the stiffness nonlinearities with a modal formulation.Two orthogonal spanwise modes describe the foreshortening effects of the wing.Dynamic linearization of the ROM under nonlinear equilibrium states is applied to a nonlinear flutter analysis,and the fully nonlinear ROM coupled with the non-planar Unsteady Vortex Lattice Method(UVLM)is applied to gust response analysis.Furthermore,extended Precise Integration Method(PIM)ensures accuracy of the dynamic equation solutions.To demonstrate applicability and accuracy of the method presented,a wind tunnel test is conducted and good agreements between theoretical and test results of nonlinear flutter speed and gust response deflection are reached.The method described in this paper is suitable for predicting the nonlinear flutter speed and calculating the gust responses of a large-aspect-ratio wing in time domain.Meanwhile,the results derived highlight the effects of geometric nonlinearities obviously.展开更多
基金Supported by the National Natural Science Foundation of China(Grant No.12161080).
文摘In this paper,the dynamics of a Leslie-Gower predator-prey model with weak nonlin-ear harvesting and prey-taxis is discussed.By comparing and analyzing the differences between ordinary differential systems and chemotaxis systems in the stability of equilibrium points,the influence mechanism of chemotaxis on the dynamic behavior of the system is deeply studied.Theoretical analysis shows that chemotaxis significantly changes the stability characteristics of the system,and the reliability of theoretical results is further verified by numerical simulation.
基金supported by the National Natural Science Foundation of China(Grant No.12475080)。
文摘We present a novel nonlinear state transition model for inositol 1,4,5-trisphosphate receptors(IP_(3)Rs)that incorporates a pre-activated state,as suggested by electron microscopy observations.Our model provides a theoretical framework for the biphasic Ca^(2+)dependence of IP_(3)Rs and accurately reproduces their experimentally observed state distribution under saturating IP_(3) conditions.By integrating receptor dynamics with cytoplasmic and endoplasmic reticulum(ER)calcium exchange,we simulate IP_(3)R-mediated Ca^(2+)oscillations governed by six key conformational states.A pivotal finding is that IP_(3)regulates these oscillations in a switch-like manner:once a critical IP_(3) concentration is reached,the system abruptly transitions to sustained,constant-amplitude oscillations that quickly terminate when the concentration exceeds a secondary threshold.These results underscore the crucial role of the pre-activated state in modulating calcium signaling.
文摘A class of nonlinear and continuous type Leontief model and its corresponding conditional input-output equation are introduced, and two basic problems under the so called positive or negative boundary assumption are presented. By approaches of nonlinear analysis some solvability results of this equation and continuous perturbation properties of the relative solution sets are obtained, and some economic significance are illustrated by the remark.
基金supported by the National Natural Science Foundation of China(Grant Nos.42150204 and 2288101)supported by the China National Postdoctoral Program for Innovative Talents(BX20230045)the China Postdoctoral Science Foundation(2023M730279)。
文摘A nonlinear multi-scale interaction(NMI)model was proposed and developed by the first author for nearly 30 years to represent the evolution of atmospheric blocking.In this review paper,we first review the creation and development of the NMI model and then emphasize that the NMI model represents a new tool for identifying the basic physics of how climate change influences mid-to-high latitude weather extremes.The building of the NMI model took place over three main periods.In the 1990s,a nonlinear Schr?dinger(NLS)equation model was presented to describe atmospheric blocking as a wave packet;however,it could not depict the lifetime(10-20 days)of atmospheric blocking.In the 2000s,we proposed an NMI model of atmospheric blocking in a uniform basic flow by making a scale-separation assumption and deriving an eddyforced NLS equation.This model succeeded in describing the life cycle of atmospheric blocking.In the 2020s,the NMI model was extended to include the impact of a changing climate mainly by altering the basic zonal winds and the magnitude of the meridional background potential vorticity gradient(PVy).Model results show that when PVy is smaller,blocking has a weaker dispersion and a stronger nonlinearity,so blocking can be more persistent and have a larger zonal scale and weaker eastward movement,thus favoring stronger weather extremes.However,when PVy is much smaller and below a critical threshold under much stronger winter Arctic warming of global warming,atmospheric blocking becomes locally less persistent and shows a much stronger westward movement,which acts to inhibit local cold extremes.Such a case does not happen in summer under global warming because PVy fails to fall below the critical threshold.Thus,our theory indicates that global warming can render summer-blocking anticyclones and mid-to-high latitude heatwaves more persistent,intense,and widespread.
基金supported by the Ministry of Higher Education and Scientific Research of Tunisia
文摘In this paper, two types of mathematical models are developed to describe the dynamics of large-scale nonlinear systems, which are composed of several interconnected nonlinear subsystems. Each subsystem can be described by an input-output nonlinear discrete-time mathematical model, with unknown, but constant or slowly time-varying parameters. Then, two recursive estimation methods are used to solve the parametric estimation problem for the considered class of the interconnected nonlinear systems. These methods are based on the recursive least squares techniques and the prediction error method. Convergence analysis is provided using the hyper-stability and positivity method and the differential equation approach. A numerical simulation example of the parametric estimation of a stochastic interconnected nonlinear hydraulic system is treated.
基金supported by the National Natural Science Foundation of China(Grant Nos.12172109,12202121,and 12302293)the China Postdoctoral Science Foundation(Grant Nos.2023M730866 and 2023T160166)+1 种基金the Guangdong Basic and Applied Basic Research Foundation(Grant No.2022A1515011492)the Shenzhen Science and Technology Program(Grant Nos.JCYJ20220531095605012,KJZD20230923115210021,and 29853MKCJ202300205).
文摘Data-driven reduced-order modeling opens new avenues of understanding,predicting,controlling,and optimizing system behavior.Simple systems may have state spaces in which sparse human-interpretable dynamical systems can be identified.This approach has been pioneered by Brunton et al.(2016,PNAS)with sparse identification of nonlinear dynamics.Complex systems,however,cannot be expected to benefit from such simple analytical descriptions.Yet,smoothness may be exploited by analytical local descriptions.In this paper,we identify a clusterwise polynomial dynamics from time-resolved snapshot data.The full state space is partitioned into clusters with a reduced-order polynomial description for each cluster and a global patching strategy.The resulting clusterwise modeling is entirely data-driven and requires no prior knowledge of the system dynamics.We illustrate the approach on the well-known chaotic Lorenz and Rössler systems,on the more challenging chaotic fluid flow dynamics of higher state-space dimensions,on a noisy electrocardiogram signal,and finally on the time evolution of the monthly sunspot number.Clusterwise modeling offers a powerful and interpretable paradigm for dynamical modeling.Nonlinear dynamics can be approximated by assembling many simple local models of different resolutions,opening new paths to understand and control intricate nonlinearities.
基金founded by the National Science and Technology Council(Taiwan)under contract NSTC113-2221-E-019-032.
文摘An optimal fuzzy tracking synthesis for nonlinear discrete-time descriptor systems is discussed through the Parallel Distributed Compensation(PDC)approach and the Proportional-Difference(P-D)feedback framework.Based on the Takagi-Sugeno Fuzzy Descriptor Model(T-SFDM),a nonlinear discrete-time descriptor system is represented as several linear fuzzy subsystems,which facilitates the linear P-D feedback technique and streamlines the fuzzy controller design process.Leveraging the P-D feedback fuzzy controller,the closed-loop T-SFDM can be transformed into a standard system that guarantees non-impulsiveness and causality for the nonlinear discrete-time descriptor system.In view of the disturbance problems,a passive performance constraint is incorporated into the fuzzy tracking synthesis to achieve dissipativity of disturbance energy.To achieve a better balance between state and control responses,the H2 performance requirement is considered and a minimization constraint is applied to optimize the H2 index.It is observed that there is a lack of research focusing on both disturbance and control input issues in nonlinear descriptor systems.Extending the Lyapunov theory,a stability analysis method is proposed for the tracking purpose with the combination of the free-weighting matrix to relax the analysis process while complying multiple performance constraints.Finally,two simulation examples are presented to demonstrate the feasibility and applicability of the proposed approach in practical control scenarios for nonlinear descriptor systems.
基金Supported by the National Natural Science Foundation of China(Grant Nos.12371393,11971150 and 11801143)Natural Science Foundation of Henan Province(Grant No.242300421047).
文摘In this paper,we propose a multiphysics finite element method for a nonlinear poroelasticity model with nonlinear stress-strain relation.Firstly,we reformulate the original problem into a new coupled fluid system-a generalized nonlinear Stokes problem of displacement vector field related to pseudo pressure and a diffusion problem of other pseudo pressure fields.Secondly,a fully discrete multiphysics finite element method is performed to solve the reformulated system numerically.Thirdly,existence and uniqueness of the weak solution of the reformulated model and stability analysis and optimal convergence order for the multiphysics finite element method are proven theoretically.Lastly,numerical tests are given to verify the theoretical results.
基金supported by the National Natural Science Foundation of China(Grant No.11974420).
文摘We study the thermodynamic properties of the classical one-dimensional generalized nonlinear Klein-Gordon lattice model(n≥2)by using the cluster variation method with linear response theory.The results of this method are exact in the thermodynamic limit.We present the single-site reduced densityρ^((1))(z),averages such as(z^(2)),<|z^(n)|>,and<(z_(1)-z_(2))^(2)>,the specific heat C_(v),and the static correlation functions.We analyze the scaling behavior of these quantities and obtain the exact scaling powers at the low and high temperatures.Using these results,we gauge the accuracy of the projective truncation approximation for theφ^(4)lattice model.
基金support from the National Natural Science Foundation of China(Grant Nos.52378411,52208404)China National Railway Group Limited Science and Technology Research and Development Program(Grant No.K2023G041).
文摘During strike-slip fault dislocation,multiple fault planes are commonly observed.The resulting permanent ground deformation can lead to profound structural damage to tunnels.However,existing analytical models do not consider multiple fault planes.Instead,they concentrate the entire fault displacement onto a single fault plane for analysis,thereby giving rise to notable errors in the calculated results.To address this issue,a refined nonlinear theoretical model was established to analyze the mechanical responses of the tunnels subjected to multiple strike-slip fault dislocations.The analytical model considers the number of fault planes,nonlinear soil‒tunnel interactions,geometric nonlinearity,and fault zone width,leading to a significant improvement in its range of applicability and calculation accuracy.The results of the analytical model are in agreement,both qualitatively and quantitatively,with the model test and numerical results.Then,based on the proposed theoretical model,a sensitivity analysis of parameters was conducted,focusing on the variables such as the number of fault planes,fault plane distance(d),fault displacement ratio(η),burial depth(C),crossing angle(β),tunnel diameter(D),fault zone width(Wf),and strike-slip fault displacement(Δfs).The results show that the peak shear force(Vmax),bending moment(Mmax),and axial force(Nmax)decrease with increasing d.The Vmax of the tunnel is found at the fault plane with the largest fault displacement.C,D,andΔfs contribute to the increases in Vmax,Mmax,and Nmax.Additionally,increasing the number of fault planes reduces Vmax and Mmax,whereas the variation in Nmax remains minimal.
基金supported by the National Nature Science Foundation of China(U21A20166)the Science and Technology Development Foundation of Jilin Province(20230508095RC)+2 种基金the Major Science and Technology Projects of Jilin Province and Changchun City(20220301033GX)the Development and Reform Commission Foundation of Jilin Province(2023C034-3)the Interdisciplinary Integration and Innovation Project of JLU(JLUXKJC2020202).
文摘Dear Editor,Aiming at the consensus tracking problem of a class of unknown heterogeneous nonlinear multiagent systems(MASs)with input constraints,a novel data-driven iterative learning consensus control(ILCC)protocol based on zeroing neural networks(ZNNs)is proposed.First,a dynamic linearization data model(DLDM)is acquired via dynamic linearization technology(DLT).
基金National Council for Scientific and Technological Development,Grant No.421278/2023-4,No.309248/2025-6。
文摘Coordinate transformation models often fail to account for nonlinear and spatially dependent distortions,leading to significant residual errors in geospatial applications.Here,we propose a residual-based neural correction(RBNC)strategy,in which a neural network learns to model only the systematic distortions left by an initial geometric transformation.By focusing solely on residual patterns,RBNC reduces model complexity and improves performance,particularly in scenarios with sparse or structured control point configurations.We evaluate the method using both simulated datasets(with varying distortion intensities and sampling strategies)and real-world image georeferencing tasks.Compared with direct neural network coordinate converters and classical transformation models,RBNC delivers more accurate and stable results under challenging conditions,while maintaining comparable performance in ideal cases.These findings demonstrate the effectiveness of residual modelling as a light-weight and robust alternative for improving coordinate transformation accuracy.
文摘Shoreline sand wave movement is one of the hot issues in coastal dynamics research.The nonlinear nearshore waves constitute the core driving force for shoreline sediment transport,significantly enhancing the lateral sediment transport intensity and exerting an important influence on shoreline sand wave movement.By using the XBeach model,the evolution process of the profile of a typical sandy beach in Haizhou Bay under the action of nonlinear waves was simulated,and the comprehensive influence of wave nonlinearity on the lateral sediment transport and sand wave movement of the beach was analyzed.The results show that the nonlinearity of waves has a relatively significant impact on the sediment transport along the shoreline of Haizhou Bay.The sediment transport in the breakwave zone 500 meters offshore is frequent.The peak line of the sand wave moves towards the shore year by year,and the peak elevation increases year by year.Within the calculation range of the model,the net sediment transport to the sea shows a slightly eroded feature in the intertidal zone of the nearshore tidal flat of Haizhou Bay.The research results have important reference significance for grasping the erosion and topographic evolution laws of the nearshore beaches of Haizhou Bay.
文摘In this paper,the authors propose a nonlinear dimension reduction technique based on Fréchet inverse regression to achieve sufficient dimension reduction for responses in metric spaces and predictors in Riemannian manifolds.The authors rigorously establish statistical properties of the estimators,providing formal proofs of their consistency and asymptotic behaviors.The effectiveness of our method is demonstrated through extensive simulations and applications to real-world datasets which highlight its practical utility for complex data with non-Euclidean structures.
文摘This paper develops a feedforward neural network based input output model for a general unknown nonlinear dynamic system identification when only the inputs and outputs are accessible observations. In the developed model, the size of the input space is directly related to the system order. By monitoring the identification error characteristic curve, we are able to determine the system order and subsequently an appropriate network structure for systems identification. Simulation results are promising and show that generic nonlinear systems can be identified, different cases of the same system can also be discriminated by our model.
基金Supported by Promoting Projects of the Industrialization of University Research of Jiangsu Province (JHZD09-35)Natural Science Research Project of Universities in Jiangsu Province (09KJD210001)Research Foundation of Huaiyin Institute of Technology(HGA0908)~~
文摘[Objective] The aim was to develop a nonlinear model of quantitative analysis of melamine content by infrared spectroscopy and provide theoretical basis for the nondestructive detection of melamine. [Method] According to dynamics,mathematical modeling and optimization theory,linear and nonlinear models were respectively set up by taking an absorption peak of 1 550 cm-1 as characteristic absorption peak. [Result] The correlation coefficient of nonlinear model was 0.922 7 and the recovery was 96%,which showed that the nonlinear model was more accurate than linearity model with correlation coefficient of 0.904 9 and recovery of 557%. [Conclusion] It is feasible to determine melamine content by using the nonlinear model quantitatively.
文摘A wavelet collocation method with nonlinear auto companding is proposed for behavioral modeling of switched current circuits.The companding function is automatically constructed according to the initial error distribution obtained through approximating the input output function of the SI circuit by conventional wavelet collocation method.In practical applications,the proposed method is a general purpose approach,by which both the small signal effect and the large signal effect are modeled in a unified formulation to ease the process of modeling and simulation.Compared with the published modeling approaches,the proposed nonlinear auto companding method works more efficiently not only in controlling the error distribution but also in reducing the modeling errors.To demonstrate the promising features of the proposed method,several SI circuits are employed as examples to be modeled and simulated.
基金Projects (51002045, 10947105) supported by the National Natural Science Foundation of ChinaProject (2010B430016) supported by the Nature Science Research Project of Education Department of Henan Province, ChinaProject (2012IRTSTHN007) supported by Program for Innovative Research Team (in Science and Technology) in the University of Henan Province, China
文摘A classic hysteretic model, Preisach-Mayergoyz model （P-M model）, was used to calculate the nonlinear elastic deformation of magnesium （Mg） and cobalt （Co）. Mg and Co samples in cylinder shape were compressively tested by uniaxial test machine to obtain their stress—strain curves with hysteretic loops. The hysteretic loops do have two properties of P-M hysteretic systems： wiping out and congruency. It is proved that P-M model is applicable for the analysis of these two metals’ hysteresis. This model was applied on Mg at room temperature and Co at 300 ℃. By the P-M model, Co and Mg nonlinear elastic deformation can be calculated based on the stress history. The simulated stress—strain curves agree well with the experimental results. Therefore, the mechanical hysteresis of these two metals can be easily predicted by the classic P-M hysteretic model.
基金The National Natural Science Foundation of China(No.11171065)the Natural Science Foundation of Jiangsu Province(No.BK2011058)
文摘In order to detect whether the data conforms to the given model, it is necessary to diagnose the data in the statistical way. The diagnostic problem in generalized nonlinear models based on the maximum Lq-likelihood estimation is considered. Three diagnostic statistics are used to detect whether the outliers exist in the data set. Simulation results show that when the sample size is small, the values of diagnostic statistics based on the maximum Lq-likelihood estimation are greater than the values based on the maximum likelihood estimation. As the sample size increases, the difference between the values of the diagnostic statistics based on two estimation methods diminishes gradually. It means that the outliers can be distinguished easier through the maximum Lq-likelihood method than those through the maximum likelihood estimation method.
基金supported by the National Key Research and Development Program of China(No.2016YFB 0200703).
文摘In this paper,a framework is established for nonlinear flutter and gust response analyses based on an efficient Reduced Order Model(ROM).The proposed method can be used to solve the aeroelastic response problems of wings containing geometric nonlinearities.A structural modeling approach presented herein describes the stiffness nonlinearities with a modal formulation.Two orthogonal spanwise modes describe the foreshortening effects of the wing.Dynamic linearization of the ROM under nonlinear equilibrium states is applied to a nonlinear flutter analysis,and the fully nonlinear ROM coupled with the non-planar Unsteady Vortex Lattice Method(UVLM)is applied to gust response analysis.Furthermore,extended Precise Integration Method(PIM)ensures accuracy of the dynamic equation solutions.To demonstrate applicability and accuracy of the method presented,a wind tunnel test is conducted and good agreements between theoretical and test results of nonlinear flutter speed and gust response deflection are reached.The method described in this paper is suitable for predicting the nonlinear flutter speed and calculating the gust responses of a large-aspect-ratio wing in time domain.Meanwhile,the results derived highlight the effects of geometric nonlinearities obviously.
